{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chapter 2, demo 1 \n",
    "\n",
    "Bayesian Data Analysis, 3rd ed\n",
    "\n",
    "\n",
    "Probability of a girl birth given placenta previa (BDA3 p. 37). 437 girls and 543 boys have been observed. Calculate and plot the posterior distribution of the proportion of girls $\\theta$, using uniform prior on $\\theta$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# import necessary packages\n",
    "\n",
    "# fast array routines for numerical calculation\n",
    "import numpy as np\n",
    "# PreliZ is a package for exploring and eliciting probability distributions\n",
    "import preliz as pz"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# set preliz style\n",
    "pz.style.use(\"preliz-doc\")\n",
    "# Change default credible interval kind and probability\n",
    "# By default PreliZ uses highest density interval (HDI) and 0.94 probability\n",
    "pz.rcParams[\"stats.ci_kind\"] = \"eti\"\n",
    "pz.rcParams[\"stats.ci_prob\"] = 0.95"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The posterior distribution is Beta(438, 544)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Instantiate the Beta distribution\n",
    "dist = pz.Beta(438, 544)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can plot the distribution using the built-in `plot_pdf` method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1150x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dist.plot_pdf(pointinterval=True);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But we want to customize the plot a bit more."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1150x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot PDF with custom legend\n",
    "ax = dist.plot_pdf(legend=r\"$p(\\theta|y,n)$\")\n",
    "# Set custom title\n",
    "ax.set_title(f'Uniform prior -> Posterior is Beta({dist.alpha:.0f}, {dist.beta:.0f})')\n",
    "# Add vertical line and annotation for general population proportion\n",
    "ax.axvline(0.485, color='C2')\n",
    "ax.annotate('proportion in general\\npopulation', (0.485 + 0.001, 14), ha='left')\n",
    "\n",
    "# shade the 95% central posterior interval\n",
    "# dist.ppf is percent point function (inverse of CDF)\n",
    "x_vals = np.linspace(*dist.ppf([0.025, 0.975]))\n",
    "ax.fill_between(x_vals, dist.pdf(x_vals), color='lightgray')\n",
    "# add text into the shaded area\n",
    "ax.text(dist.median(), 8, \"95%\", horizontalalignment='center', fontsize=18)\n",
    "# # add labels and title\n",
    "ax.set_xlabel(r'$\\theta$');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Authors:\n",
    "- Aki Vehtari <aki.vehtari@aalto.fi>\n",
    "- Tuomas Sivula <tuomas.sivula@aalto.fi>\n",
    "- Osvaldo A. Martin <osvaldo.martin@aalto.fi>"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "bda_py_demos",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
